Eigenfrequencies of nonisotropic fractal drums

Abstract

Let Γ be a regular nonisotropic fractal. The aim of the paper is to investigate the distribution of the eigenvalue of the fractal differential operator ( - Δ ) - 1 ∘ tr Γ acting in the anisotropic Sobolev space W 2 1 , α ( R 2 ) , where ( - Δ ) - 1 is the inverse of the Dirichlet Laplanian in R 2 and tr Γ is closely related to the trace operator tr Γ .